Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+6y &= -4 \\ -2x+2y &= -3\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 2x-3$ Divide both sides by $2$ to isolate $y$ $y = {x - \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $-5x+6({x - \dfrac{3}{2}}) = -4$ $-5x + 6x - 9 = -4$ Simplify by combining terms, then solve for $x$ $1x - 9 = -4$ $1x = 5$ $x = 5$ Substitute $5$ for $x$ back into the top equation. $-5( 5)+6y = -4$ $-25+6y = -4$ $6y = 21$ $y = \dfrac{7}{2}$ The solution is $\enspace x = 5, \enspace y = \dfrac{7}{2}$.